Question

A circular wheel comprises a ring of radius $R$ and mass $M$ and three spokes of mass $m$ and length $R$ each. The moment of inertia of the wheel about its axis passing through its centre and perpendicular to its plane is

• A. $(M+\frac{m}{4})R^2$
• B. $(M+m)R^2$
• C. $(M+3m)R^2$
• D. $\left(\frac{M+m}{2}\right)R^2$

Answer 1

The correct option is B $(M+m)R^2$

Moment of inertia of the wheel is
$I=I_{ring}+3I_{spoke}=M{R}^2+3\left(\frac{m{R}^2}{3}\right)=(M+m)R^2$